Games with creatures

Saharon Shelah; Jindřich Zapletal

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 1, page 9-21
  • ISSN: 0010-2628

Abstract

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Many forcing notions obtained using the creature technology are naturally connected with certain integer games.

How to cite

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Shelah, Saharon, and Zapletal, Jindřich. "Games with creatures." Commentationes Mathematicae Universitatis Carolinae 44.1 (2003): 9-21. <http://eudml.org/doc/249148>.

@article{Shelah2003,
abstract = {Many forcing notions obtained using the creature technology are naturally connected with certain integer games.},
author = {Shelah, Saharon, Zapletal, Jindřich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {creature forcing; determinacy; creature forcing; determinacy},
language = {eng},
number = {1},
pages = {9-21},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Games with creatures},
url = {http://eudml.org/doc/249148},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Shelah, Saharon
AU - Zapletal, Jindřich
TI - Games with creatures
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 1
SP - 9
EP - 21
AB - Many forcing notions obtained using the creature technology are naturally connected with certain integer games.
LA - eng
KW - creature forcing; determinacy; creature forcing; determinacy
UR - http://eudml.org/doc/249148
ER -

References

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  1. Jech T., Set Theory, Academic Press, San Diego, 1978. Zbl1007.03002MR0506523
  2. Kechris A., On a notion of smallness for subsets of the Baire space, Trans. Amer. Math. Soc. 229 (1977), 191-207. (1977) Zbl0401.03022MR0450070
  3. Anthony Martin D., A purely inductive proof of Borel determinacy, Number 42 in Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence, 1985, pp.303-308. MR0791065
  4. Roslanowski A., Shelah S., Norms on possibilities I: forcing with trees and creatures, Memoirs Amer. Math. Soc. 141, 1999. Zbl0940.03059MR1613600
  5. Shelah S., Viva la difference I: Nonisomorphism of ultrapowers of countable models, in Set Theory of the Continuum, vol. 26 of Mathematical Sciences Research Institute Publications, Springer Verlag, 1992, pp.357-405. MR1233826
  6. Bartoszynski T., Judah H., Set Theory. On the Structure of the Real Line, A K Peters, Wellesley, MA, 1995. Zbl0834.04001MR1350295
  7. Zapletal J., Cardinal Invariants and Descriptive Set Theory, Memoirs Amer. Math. Soc., submitted. 
  8. Zapletal J., Forcing with ideals of closed sets, Comment. Math. Univ. Carolinae 43.1 (2002), 181-188. (2002) MR1903318

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